solve the equation for 0≤ x < 2 pie

We need to isolate x like any algebraic equation:

4sin(x) = -1 + 2sin(x)

4sin(x) - 2sin(x) = -1

2sin(x) = -1

sin(x) = -1/2

x = sin

^{-1}(-1/2)x = -.524

But since the answer must be between 0 and 2pi, you add 2pi to the answer to get it in the right range:

-.524 + 2pi =

**5.759**